Balls in a bin (w/ a twist)

prov_in_stl

I have a 15 balls and 8 bins. Each bin can only hold 4 balls. If throw the 15 balls in the bins (random) and all the balls land in the bins, how do i find the distribution of balls/bin. eg. #4 bins with 3 balls, #1 bin with 1 ball etc.

Thanks!

HallsofIvy

You will need to find the total number of ways that you can have 8 numbers, each at least 1, none larger than 4, that add to 15.

prov_in_stl

Yes. I should have mentioned that I figure that part out but was wondering if there was a simplified formula to do the same? Because, I would also have to be able to count the number of times each integer between 1 and 4 occurs in the this combination.

Any help would be appreciated.